The first thing to realize about space is that it's a LOT of nothing. Beyond comprehension. Stuff that escapes the atmosphere/gravity well gets dispersed across the endless void until it is nigh-undetectable. Every atom that makes up our entire solar system could be fissioned down to hydrogen and helium and dispersed into space and statistically nothing would change.

It has a few ways that it can "go" when it reaches up high enough in the atmosphere. It's either just hanging around the planets upper atmosphere as really low density gas, or it's swept away by the solar wind out into space until it's caught by some other gravity well.
(Someone else might know wether solar wind is strong enough to push it out of the solar system, but I reckon most of it gets pulled in by the sun)

It’s important to remember that space is very, very empty, but it isn’t completely empty. Helium in space follows the same rules of everything else; it’s at the whims of all the forces acting on it, particularly gravity and solar winds.

Helium will escape the atmosphere and then be stuck, since it can’t escape Earth’s gravity. But then it will get pushed by solar winds away from Earth. Helium will follow solar winds around, ultimately reaching the edge of our solar system, though it may take a circuitous route to get there.

Helium is pushed up through the atmosphere by the atmosphere, So it just float on top as it's still attracted to earth. In order for it to leave some force would have to be applied to counteract earth's gravity, this can come in the form of solar radiation if the helium becomes ionized or from the atmosphere of the sun.

How fast each volatile element escapes from a celestial body depends on the escape velocity of the body and the temperature in the upper atmosphere. Stars and gas giants have much higher escape velocities than Earth so typically retain their hydrogen and helium, although in some cases even these massive objects can undergo significant mass loss.

But as for where the helium (and hydrogen) that escapes goes: Into the interplanetary medium, and potentially into the interstellar medium after that. From the Sun, the solar wind carries off about a million tonnes of hydrogen and helium plasma every second, which is nothing compared to the overall mass of the Sun; since formation, only a fraction of a percent of its mass has been lost this way. The solar wind moves outwards, interacting with other gas and dust particles in the interplanetary medium, and eventually merges into the interstellar medium at the heliopause about 100 AU out.

Nobody is mentioning that helium doesn't float away out of the sun. Helium floats because the other gasses in our atmosphere are heavier than it, so it floats on top like marshmallows in cocoa to get sucked into space. A key factor here is that the sun is mostly hydrogen so helium being twice as heavy sinks to the middle instead of floating on top.